Information on Result #547981
There is no linear OA(825, 52, F8, 22) (dual of [52, 27, 23]-code), because construction Y1 would yield
- OA(824, 28, S8, 22), but
- the linear programming bound shows that M ≥ 41 859056 504156 535174 201344 / 8073 > 824 [i]
- linear OA(827, 52, F8, 24) (dual of [52, 25, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(827, 36, F8, 24) (dual of [36, 9, 25]-code), but
- residual code [i] would yield OA(83, 11, S8, 3), but
- 1 times truncation [i] would yield OA(82, 10, S8, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 71 > 82 [i]
- 1 times truncation [i] would yield OA(82, 10, S8, 2), but
- residual code [i] would yield OA(83, 11, S8, 3), but
- discarding factors / shortening the dual code would yield linear OA(827, 36, F8, 24) (dual of [36, 9, 25]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(826, 53, F8, 23) (dual of [53, 27, 24]-code) | [i] | Truncation | |
| 2 | No linear OOA(826, 52, F8, 2, 23) (dual of [(52, 2), 78, 24]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(825, 52, F8, 2, 22) (dual of [(52, 2), 79, 23]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(825, 52, F8, 3, 22) (dual of [(52, 3), 131, 23]-NRT-code) | [i] | ||
| 5 | No digital (3, 25, 52)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(834, 59, F8, 30) (dual of [59, 25, 31]-code) | [i] | Construction Y1 (Bound) | |